This paper addresses the problem of H-infinity state feedback control design for discrete-time Markov jump linear systems (MJLS) with uncertain transition probability matrix. The main novelty is that, differently from the existing approaches in the literature, the proposed conditions allow the use of polynomially parameter-dependent Lyapunov matrices to certify the closed-loop stability of the MJLS. Therefore, the method is able to provide H-infinity controllers in cases where the other techniques fail. The synthesis conditions are given in terms of linear matrix inequality relaxations. Examples illustrate the main advantages of the proposed control design method when compared to other approaches from the literature. (C) 2014 Elsevier Ltd. All rights reserved.